The Weibull-exponential {Rayleigh} Distribution: Theory and Applications
Abstract
This study introduces a new distribution in the family of generalized exponential distributions generated using the transformed-transformer method. Some properties of the distribution are presented. The new distribution has three parameters and they are estimated numerically using the BGFS iterative method implemented in R software. Two real sets of data are adopted to demonstrate the flexibility and potential applications of the new distribution.
References
R. Al-Aqtash, C. Lee and F. Famoye, Gumbel-Weibull distribution: Properties and application, Journal of Modern Applied Statistical Methods 13(2) (2014), 201-225. https://doi.org/10.22237/jmasm/1414815000
M. Aldeni, C. Lee and F. Famoye, Families of distributions arising from the quantile of generalized lambda distribution, Journal of Statistical Distributions and Applications 4(25) (2017), 1-18. https://doi.org/10.1186/s40488-017-0081-4.
M.A. Aljarrah, C. Lee and F. Famoye, A new method of generating T-X family of distributions using quantile functions, Journal of Statistical Distributions and Applications 1(2) (2014), 1-17. http://www.jsdajournal.com/content/1/1/2
M. Almheidat, F. Famoye and C. Lee, Some generalized families of Weibull distribution: Properties and applications, International Journal of Statistics and Probability 4(3) (2015), 18-35. http://dx.doi/10.5539/ijsp.v4n3p18
A. Alzaatreh, C. Lee and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013a), 63-79. https://doi.org/10.1007/s40300-013-0007-y
A. Alzaatreh, F. Famoye and C. Lee, Weibull-Pareto distribution and applications, Comm. Statist. Theory Methods 42(9) (2013b), 1673-1691. http://dx.doi.org/10.1080/03610926.2011.599002
A. Alzaatreh, C. Lee and F. Famoye, T-normal family of distributions: a new approach to generalize the normal distribution, Journal of Statistical Distributions and Applications 1(16) (2014), 1-18. http://www.jsdajournal.com/content/1/1/16
A. Alzaatreh, C. Lee and F. Famoye, Family of generalized gamma distributions: Properties and Applications, Hacet. J. Math. Stat. 45(3) (2016a), 869-886. https://doi.org/10.15672/HJMS.20156610980
A. Alzaatreh, C. Lee, F. Famoye and I. Ghosh, The generalized Cauchy family of distributions with applications, Journal of Statistical Distributions and Applications 3 (2016b), Article No. 12. https://doi.org/10.1186/s40488-016-0050-3
A. Alzahal, F. Famoye and C. Lee, Exponentiated T-X family of distributions with some applications, International Journal of Statistics and Probability 2(3) (2013), 31-49. http://dx.doi.org/10.5539/ijsp.v2n3p31
M.I. Ekum, M.O. Adamu and E.E. Akwarawak, T-Dagum: A way of generalizing Dagum distribution using Lomax quantile function, J. Probab. Stat. (2020), Art. ID 1641207, 17 pp. https://doi.org/10.1155/2020/1641207
M.G. Bader and A.M. Priest, Statistical aspects of fiber and bundle strength in hybrid composites, T. Hayashi, K. Kawata and S. Umekawa, eds., Progress in Science and Engineering Composites, pp. 1129-1136, Tokyo: ICCM-IV, 1982.
K. Fatima and S.P. Ahmad, Statistical properties of Exponential Rayleigh distribution and its application to medical sciences and engineering, International Conference on Recent Innovations in Science, Agriculture, Engineering and Management University College of Computer Applications Guru Kashi University, Bathinda, Punjab (India) (2017), 491-506.
I.S. Grandshteyn and I.M. Ryzhik, Table of Integrals, Series, and Product, 8th ed., Elsevier, Inc., 2015.
D. Hamed, F. Famoye, and C. Lee, On families of generalized Pareto distributions: properties and applications, Journal of Data Science (2018), 377-396. https://doi.org/10.6339/JDS.201804_16(2).0008
F. Jamal, M.A. Aljarrah, M.H. Tahir and M.A. Nasir, A new extended generalized Burr-III family of distributions, Tbilis Math. J. 11 (2018), 59-78.
C. Lee, F. Famoye and A. Alzaatreh, Methods for generating families of univariate continuous distributions in the recent decades, WIREs Computational Statistics 5 (2013), 219-238. https://doi.org/10.1002/wics.1255
F. Merovci and I. Elbatal, Weibull Rayleigh distribution: Theory and Applications, Appl. Math. Inf. Sci. 9(4) (2015), 2127-2137. http://dx.doi.org/10.12785/amis/090452
V.H. Moll, The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of logarithms and exponentials, Sci. Ser. A Math. Sci. (N.S.) 15(1) (2007), 31-36. http://arxiv.org/abs/0705.0175v1
D.N.P. Murthy, M. Xie and R. Jiang, Weibull Models, John Wiley, New Jersey, 2004.
P. Oguntunde, O.S. Balogun, H.I. Okagbue and S.A. Bishop, The Weibull-Exponential distribution: Its properties and applications, Journal of Applied Sciences 15(11) (2015), 1305-1311. https://doi.org/10.3923/jas.2015.1305.1311
P. Osatohanmwen, F.O. Oyegue and S.M. Ogbonmwan, A new member from the T-X family of distributions: The Gumbel-Burr XII distribution and its Properties, Sankhya A 81 (2019), 298-322. https://doi.org/10.1007/s13171-017-0110-x
C.E. Shanon, A mathematical theory of communication, Mobile Computing and Communications Review 5 (1948). https://doi.org/10.1145/584091.584093
G.R. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, John Wiley and Sons, New York, 1986.
M.H. Tahir, G.M. Cordeiro, A. Alzaatreh, M. Monsoor and M. Zubair, The logistic-X family of distributions and its applications, Comm. Statist. Theory Methods 45 (2016), 7326-7349. http://dx.doi.org/10.1080/03610926.2014.980516
This work is licensed under a Creative Commons Attribution 4.0 International License.